Nii-MALA：一种具有径向速度基准的快速 Metropolis-Adjusted Langevin 采样器
Nii-MALA: A Fast Metropolis-Adjusted Langevin Sampler with Radial Velocity Benchmarks
- Anhui Normal University（安徽师范大学）
- Northwestern University（西北大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出 Nii-MALA，一种基于 MPI 并行和自动微分的快速 Langevin 采样器，在低维高斯分布上优于随机游走，但在径向速度轨道拟合等复杂函数上效率低于并行回火。
AI中文摘要：
马尔可夫链蒙特卡洛方法广泛应用于天文学和天体物理学中的模型评估与参数拟合，催生了大量实现各种采样技术的即用型软件包。对于涉及众多独立目标的大规模分析，计算效率至关重要，因为它决定了整体运行时间。我们介绍了 Nii-MALA，一种高性能的 Metropolis-Adjusted Langevin 算法 C 语言实现，该实现利用消息传递接口进行并行化，并集成了自动微分后端用于梯度评估。该代码通过配置文件提供灵活控制，允许用户为并行链中的所有模型参数指定提议步长。我们在 15 维和 30 维高斯分布以及双峰分布上验证了其有效性，并进一步使用 51 Pegasi b 的径向速度数据将其与多种其他代码进行了基准测试。我们的基准测试证实，在获取有效样本量方面，Langevin 采样比随机游走采样更高效，尤其是随着目标函数维度的增加。当与高效的自动微分库配合使用时，这种算法优势可以得到有效利用。然而，对于天文学中常见的复杂函数（如径向速度轨道拟合），有效样本量分析显示，依赖导数的 Langevin 采样器的效率低于并行回火或其他替代采样方法。
英文摘要：
Markov chain Monte Carlo is widely used for model assessment and parameter fitting in astronomy and astrophysics, leading to numerous ready-to-use packages implementing various sampling techniques. For large-scale analyses involving many individual targets, computational efficiency becomes paramount, as it dictates the overall runtime. We introduce Nii-MALA, a high-performance C implementation of the Metropolis-Adjusted Langevin Algorithm, which leverages Message Passing Interface for parallelization and incorporates automatic differentiation backends for gradient evaluation. The code offers flexible control via a configuration file, allowing users to specify the proposal step sizes for all model parameters across parallel chains. We validate its effectiveness on 15- and 30-dimensional Gaussian distributions and a bimodal distribution, and further benchmark it against several other codes using radial velocity data from 51 Pegasi b. Our benchmarks confirm the efficiency of Langevin sampling over random-walk sampling in obtaining the effective sample size, particularly as the dimensionality of the target function increases. This algorithmic advantage can be effectively leveraged when paired with an efficient automatic differentiation library. However, for complex functions commonly encountered in astronomy---such as radial velocity orbital fitting---the derivative-dependent Langevin sampler shows lower efficiency than parallel tempering or alternative sampling approaches, as revealed by effective sample size analysis.
